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Formula
Solve the equation
Answer
Graph
$y = \dfrac { 1 } { 2 } + \dfrac { 1 } { 5 }$
$y = \dfrac { 1 } { x }$
Asymptote
$y = 0$, $x = 0$
Standard form
$y = \dfrac { 1 } { x }$
Domain
$y \neq 0$
Range
$x \neq 0$
$\dfrac{ 1 }{ 2 } + \dfrac{ 1 }{ 5 } = \dfrac{ 1 }{ x }$
$x = \dfrac { 10 } { 7 }$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 5 } } = \color{#FF6800}{ \dfrac { 1 } { x } }$
 Reverse the left and right terms of the equation (or inequality) 
$\color{#FF6800}{ \dfrac { 1 } { x } } = \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 5 } }$
$\color{#FF6800}{ \dfrac { 1 } { x } } = \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 5 } }$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 5 } } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ x } \left ( \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 5 } } \right ) \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ \dfrac { 7 x } { 10 } } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 1 } = \color{#FF6800}{ \dfrac { 7 x } { 10 } } \\ x \neq 0 \end{cases}$
 Reverse the left and right terms of the equation (or inequality) 
$\begin{cases} \color{#FF6800}{ \dfrac { 7 x } { 10 } } = \color{#FF6800}{ 1 } \\ x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ \dfrac { 7 x } { 10 } } = \color{#FF6800}{ 1 } \\ x \neq 0 \end{cases}$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \end{cases} \\ x \neq 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \end{cases} \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 If there is a system of equations (inequality) in the system of equations (inequality), take it out. 
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Simplify the expression 
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \\ 10 \neq 0 \\ x \neq 0 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ 10 \neq 0 \\ x \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
 Substitute $x = \dfrac { 10 } { 7 }$ for unresolved equations or inequalities 
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ \dfrac { 10 } { 7 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = \dfrac { 10 } { 7 } \\ \color{#FF6800}{ 10 } \neq \color{#FF6800}{ 0 } \\ \dfrac { 10 } { 7 } \neq 0 \end{cases}$
 There are infinitely many solutions if both sides of $\ne$ are different. 
$\begin{cases} x = \dfrac { 10 } { 7 } \\ \text{There are countless solutions} \\ \dfrac { 10 } { 7 } \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ \text{There are countless solutions} \\ \color{#FF6800}{ \dfrac { 10 } { 7 } } \neq \color{#FF6800}{ 0 } \end{cases}$
 Ignore the cases where the system of equations where there are infinitely many solutions. 
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ \color{#FF6800}{ \dfrac { 10 } { 7 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = \dfrac { 10 } { 7 } \\ \color{#FF6800}{ \dfrac { 10 } { 7 } } \neq \color{#FF6800}{ 0 } \end{cases}$
 There are infinitely many solutions if both sides of $\ne$ are different. 
$\begin{cases} x = \dfrac { 10 } { 7 } \\ \text{There are countless solutions} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } } \\ \text{There are countless solutions} \end{cases}$
 Ignore the cases where the system of equations where there are infinitely many solutions. 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { 7 } }$
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